Details

sample75.0ms

Algorithm

intervals

Results

22.0ms	38×	body	1280	valid
19.0ms	54×	body	640	valid
10.0ms	150×	body	80	valid
6.0ms	26×	body	320	valid
4.0ms	84×	body	80	nan
3.0ms	19×	body	160	valid

simplify109.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (7.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	106	6
4	304	4
5	774	4
6	4142	4
7	5001	4

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
6.3b	(pow (/ x (+ x y)) x)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

27.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
7.0ms	(pow (/ x (+ x y)) x)

series391.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(/ (pow (/ x (+ x y)) x) x)
37.0ms	(/ x (+ x y))
223.0ms	(pow (/ x (+ x y)) x)

simplify67.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	537	1436
1	2640	1406
2	5001	1406

prune373.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
2.4b	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

61×	`unpow-prod-down`
51×	`cbrt-prod`
48×	`*-un-lft-identity`
43×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `pow-exp` `flip-+`
6×	`pow1` `pow-unpow` `distribute-lft-out`
5×	`div-exp`
4×	`frac-times` `prod-exp` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `div-inv` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
12.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
18.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series857.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(cbrt x)
171.0ms	(cbrt x)
254.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
262.0ms	(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify58.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	691	1334
1	2164	1266
2	5001	1235

prune388.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.0b	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.0b	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.0b	(pow (/ (cbrt x) (cbrt (+ x y))) x)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

54×	`unpow-prod-down`
48×	`cbrt-prod`
47×	`*-un-lft-identity`
42×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`add-exp-log`
7×	`pow1`
6×	`distribute-lft-out`
5×	`pow-unpow`
4×	`pow-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `sqr-pow`
2×	`cbrt-div` `associate-/r/`
1×	`flip3-+` `pow1/3` `div-exp` `flip-+` `div-inv`

Counts

4 → 104

Calls

4 calls:

0.0ms	(cbrt x)
1.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
1.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
16.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)

series497.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
26.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
26.0ms	(pow (fabs (/ (cbrt x) (cbrt (+ x y)))) (* 2 (/ x 2)))
262.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)

simplify53.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	540	1207
1	1915	1176
2	5001	1108

prune407.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (* -1 y)) x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log`
1×	`pow1` `cbrt-undiv` `exp-neg` `frac-2neg` `mul-1-neg` `div-exp` `clear-num` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 28

Calls

1 calls:

3.0ms

(/ (exp (* -1 y)) x)

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(/ (exp (* -1 y)) x)

simplify53.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	114	186
1	303	172
2	1465	170
3	5003	170

prune59.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes59.0ms

Accuracy

97.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 5.7b

bsearch71.0ms

Steps

Iters	Range		Point
4	0.0019924046320714574	0.003211336228265424	0.003173244615884362
5	-1.2065450589787464e+41	-3.918237991634595e+40	-3.9722026627658497e+40

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	27
1	32	27

end0.0ms

sample2.4s

Algorithm

intervals

Results

873.0ms	1509×	body	1280	valid
535.0ms	1448×	body	640	valid
343.0ms	4885×	body	80	valid
203.0ms	812×	body	320	valid
146.0ms	2998×	body	80	nan
74.0ms	451×	body	160	valid